MathDB
Collinear Centers and Midarcs

Source: 2021 APMO P3

June 9, 2021
geometrycircumcircleAPMO

Problem Statement

Let ABCDABCD be a cyclic convex quadrilateral and Γ\Gamma be its circumcircle. Let EE be the intersection of the diagonals of ACAC and BDBD. Let LL be the center of the circle tangent to sides ABAB, BCBC, and CDCD, and let MM be the midpoint of the arc BCBC of Γ\Gamma not containing AA and DD. Prove that the excenter of triangle BCEBCE opposite EE lies on the line LMLM.
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